solving rational equations
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Solving Rational Equations. Lesson 4. Objectives. Find the values that will make a rational expression undefined(excluded values) Solve rational equations. Algebraic Fraction/Rational Expression. - PowerPoint PPT PresentationTRANSCRIPT
ObjectivesFind the values that will make a rational expression undefined(excluded values)
Solve rational equations
Algebraic Fraction/Rational Expression
Since a RE indicates division, we cannot replace the variables in a denominator with numbers that make the denominator zero.
Solving Rational Equations
1. Identify and exclude any values that will make the denominator zero.
2. Multiply both sides by the LCD and simplify (this will eliminate all denominators).
3. Solve the resulting equation.4. Check all solutions in the original
equation.
Example 13
Check:We need 2b – 5 ≠ 0 and b – 3 ≠ 0which means b ≠ 5/2 and b ≠ 3.
multiply by LCD.
Simplify – denominators are eliminated
Distribute
Solve for b.
Solve for m.
2(m – 1) – m = 4 2m - 2 - m = 4 m = 6
Simplify – denominators are eliminated
Distribute
Solve for m.
multiply by LCD.
Solve for x.
x2 – 3x + 12 = x – 3 + 4xx2 – 8x + 15 = 0(x – 3)(x – 5) = 0x = 3 or x = 5
Simplify – denominators are eliminatedSet equation equal to zero.
Factor.Zero factor property
multiply by LCD.
x = 3 is an extraneous root and x =5 is the only solution.
SOLVING RATIONAL EQUATIONS• Find the LCD• Multiply both sides of the equation
by the LCD.• Solve using APE/MPE and/or• Solve by factoring.• Cross check solutions with
restrictions